The profile of a decorative architectural arch, as shown in the cross-section of a building design, is modeled using a coordinate system where the vertical height HHH (in decametres) is given by the equation H=x2−9x+22H = x^2 - 9x + 22H=x2−9x+22, where x x\,x is the horizontal distance from a vertical support wall.
The arch is supported by a horizontal beam at a constant height of H=4H = 4H=4 decametres, which we will call line LLL.
The arch intersects the support wall at point DDD.
Write down the coordinates of point DDD.
The arch intersects the horizontal beam L L\,L at the points E E\,E and FFF, as shown.
Find the xxx-coordinate of E E\,E and the xxx-coordinate of FFF.
Two specific design regions are identified:
Given that Area of R1Area of R2=k\displaystyle \frac{\text{Area of } R_1}{\text{Area of } R_2} = kArea of R2Area of R1=k,
use algebraic integration to find the exact value of kkk, giving your answer as a simplified fraction.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
